Yuchun Hua, Yuelong Tang, Zhaohui Chen, A rectangular MFE combined with variational discretization for elliptic optimization problems with integral constraints, Vol. 2026 (2026), No. 12, pp. 1-12

Full Text: PDF
DOI: 10.23952/jnfa.2026.12

Received November 6, 2025; Accepted March 23, 2026; Published May 7, 2026

Abstract. This paper investigates the use of a rectangular mixed finite element combined with variational discretization to solve elliptic optimization problems with integral constraints. The state and co-state variables are discretized by using the $Q_{k-1,k}\times Q_{k,k-1}-Q_{k,k}$ mixed finite element. The control variable is obtained via a variational discretization technique. Under appropriate regularity assumptions, convergence and superconvergence results are rigorously derived by introducing some auxiliary variables and projection operators. Some examples are given to confirm the results of the theoretical analysis.

How to Cite this Article:
Y. Hua, Y. Tang, Z. Chen, A rectangular MFE combined with variational discretization for elliptic optimization problems with integral constraints, J. Nonlinear Funct. Anal. 2026 (2026) 12.